Title: Scattering methods for skew-product parabolic maps
Speaker: Liz Vivas
Speaker Info: Ohio State University
Brief Description:
Special Note: Midwest Dynamical Systems Conference
Abstract:
A classical tool in the study of the dynamics of a given map $f$ is to conjugate it to a simpler one $g$. One way to obtain a conjugacy is to take limits of composition and precompositions of this two maps $f^{n}\circ g^{-n}$. This standard procedure does not always converge. We will survey a list of results in which this method is used and introduce a new setting in which we obtain convergence: the case of parabolic skew product maps in $\mathbb{C}^2$. We study the dynamics of our map in a neighborhood of the invariant fiber. We give explicit formulas for the parametrizations of the "unstable" manifolds in this context, as well as for the "Fatou coordinates" of the incoming and outgoing basins of F.Date: Sunday, November 05, 2017